code: def test_ddm_charpoly():
      A = []
      assert ddm_berk(A, ZZ) == [[ZZ(1)]]
  
      A = [
          [ZZ(1), ZZ(2), ZZ(3)],
          [ZZ(4), ZZ(5), ZZ(6)],
          [ZZ(7), ZZ(8), ZZ(9)],
      ]
      Avec = [[ZZ(1)], [ZZ(-15)], [ZZ(-18)], [ZZ(0)]]
      assert ddm_berk(A, ZZ) == Avec
  
      A = DDM([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
      raises(DMShapeError, lambda: ddm_berk(A, ZZ))
  
file_path: sympy/sympy/polys/matrices/tests/test_dense.py
imports: from sympy.testing.pytest import raises
  from sympy.polys import ZZ, QQ
  from sympy.polys.matrices.ddm import DDM
  from sympy.polys.matrices.dense import ddm_transpose, ddm_iadd, ddm_isub, ddm_ineg, ddm_imatmul, ddm_imul, ddm_irref, ddm_idet, ddm_iinv, ddm_ilu, ddm_ilu_split, ddm_ilu_solve, ddm_berk
  from sympy.polys.matrices.exceptions import DMDomainError, DMNonInvertibleMatrixError, DMNonSquareMatrixError, DMShapeError
label_desc: Use image node_id 13 for calling a global function with example usage: test_ddm_charpoly() without return types